10 pts 7. Use algebra to rewrite the integrand; then integrate and simplify. $$ \int \frac{x-4}{\sqrt{x}} dx $$ A) $$ \frac{2}{3} x\sqrt{x}-4\sqrt{x}+C $$ B) $$ \frac{2}{3} x\sqrt{x}-8\sqrt{x}+C $$ C) $$ \frac{2}{3} x\sqrt{x}-12\sqrt{x}+C $$ D) $$ \frac{1}{2} x^2-12\sqrt{x}+C $$ E) $$ \frac{1}{2} x^2-8\sqrt{x}+C $$
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Step 1
First, we rewrite the integrand using algebra. We can split the fraction into two terms: $$ \frac{x-4}{\sqrt{x}} = \frac{x}{\sqrt{x}} - \frac{4}{\sqrt{x}} $$ Step 2: Simplify each term. For the first term, $$ \frac{x}{\sqrt{x}} = \frac{x}{x^{1/2}} = x^{1 - 1/2} Show more…
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